In this paper we propose and evaluate the Block Max WAND with Candidate Selection and Preserving Top-K Results algorithm, or BMW-CSP. It is an extension of BMW-CS, a method previously proposed by us. Although very efficient, BMW-CS does not guarantee preserving the top-k results for a given query. Algorithms that do not preserve the top results may reduce the quality of ranking results in search systems. BMW-CSP extends BMW-CS to ensure that the top-k results will have their rankings preserved. In the experiments we performed for computing the top-10 results, the final average time required for processing queries with BMW-CSP was lesser than the ones required by the baselines adopted. For instance, when computing top-10 results, the average time achieved by MBMW, the best multi-tier baseline we found in the literature, was 36.29 ms per query, while the average time achieved by BMW-CSP was 19.64 ms per query. The price paid by BMW-CSP is an extra memory required to store partial scores of documents. As we show in the experiments, this price is not prohibitive and, in cases where it is acceptable, BMW-CSP may constitute an excellent alternative query processing method.